Geometry and topology behind linear differential equations

The Stokes phenomenon refers to the fact that the analytic continuation of asymptotic solutions to certain systems of linear ODEs cannot preserve their asymptotic behaviour. In this talk, we will introduce this phenomenon by studying some examples. After that, we will investigate the geometry (meromorphic connections) and topology (Stokes local systems) behind it, and we will discuss the associated Riemann-Hilbert correspondence that relates them. Finally, we will go beyond this correspondence and illustrate an irregular nonabelian Hodge correspondence. Based on a recent joint work with Hao Sun.